Frequently, the canister cover will be very difficult to break free. Use a breaker bar with CAUTION! You may need a low profile' socket due to the limited space available.
If you loosen the filter canister cover enough to break the seal, it will help drain the oil from the filter as you drain the oil pan. Less mess later!
When replacing the O-ring, save the old one just in case (will explain later).
When replacing the O-ring on the canister cover, make sure you lubricate the O-ring with PLENTY of fresh oil before you install it, and lubricate again after it is in place. If you fail to do this, the O-ring will bunch up and cause a leak!
The new oil filter should be 'pre-seated' into the base and cover before installation. Take the filter (plastic side down) and press firmly into the base until it is fully seated. Remove and do the same into the cannister cover. This reduces the resistance from initial seating. You can leave the filter seated into the cover and screw the cover back onto the base, or you can leave the filter in the base fully seated and screw the cover back onto the base.
The early MINI with production dates up to 07/2004 has a couple extra pieces inside the oil filter cannister cover - a spring and plastic cage. These items were eliminated on the later models after 07/2004. This article explains the differences and what to do if you lose some of these parts.